R Notebook

library(robust)

Loading required package: fit.models

train <- train %>%
  filter(price > quantile(price, 0.01), price < quantile(price, 0.99)) %>%
  filter(floor_area > quantile(floor_area, 0.01), floor_area < quantile(floor_area, 0.99))

Let’s build a simple linear model with floor_area, num_rooms, category + is_business

summary(m1)

Call:
lm(formula = price ~ floor_area + rooms_num + category + is_business, 
    data = train)

Residuals:
    Min      1Q  Median      3Q     Max 
-965142 -106788  -28235   72750 1754924 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    -164040.83    7491.88 -21.896  < 2e-16 ***
floor_area                        3912.99      45.52  85.954  < 2e-16 ***
rooms_num                        15644.40    1551.86  10.081  < 2e-16 ***
categoryMieszkanie na sprzedaż  240446.49    4646.16  51.752  < 2e-16 ***
is_business                      29132.25    4118.09   7.074 1.54e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 203300 on 30665 degrees of freedom
  (31 observations deleted due to missingness)
Multiple R-squared:  0.3993,    Adjusted R-squared:  0.3992 
F-statistic:  5096 on 4 and 30665 DF,  p-value: < 2.2e-16

Plot1

\[ (y_i - \hat{y_i}, \hat{y}_i) \]

Now, we will calculate robust model with MASS::rlm

summary(m1)

Call:
lm(formula = price ~ floor_area + rooms_num + category + is_business, 
    data = train)

Residuals:
    Min      1Q  Median      3Q     Max 
-965142 -106788  -28235   72750 1754924 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    -164040.83    7491.88 -21.896  < 2e-16 ***
floor_area                        3912.99      45.52  85.954  < 2e-16 ***
rooms_num                        15644.40    1551.86  10.081  < 2e-16 ***
categoryMieszkanie na sprzedaż  240446.49    4646.16  51.752  < 2e-16 ***
is_business                      29132.25    4118.09   7.074 1.54e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 203300 on 30665 degrees of freedom
  (31 observations deleted due to missingness)
Multiple R-squared:  0.3993,    Adjusted R-squared:  0.3992 
F-statistic:  5096 on 4 and 30665 DF,  p-value: < 2.2e-16

sum(m2$w < 1) / NROW(m2$w)

[1] 0.2250408

plot(m2$y, m2$w, xlab = "Price", ylab = "Huber weight", 
     main = "Distribution of prices and Huber weights")

plot(m2$x[,"floor_area"], m2$w, xlab = "Floor area", ylab = "Huber weight", 
     main = "Distribution of floor area and Huber weights")

summary(m3)

Call: rlm(formula = price ~ floor_area + rooms_num + category + is_business, 
    data = train, psi = psi.bisquare, y.ret = TRUE)
Residuals:
    Min      1Q  Median      3Q     Max 
-804133  -79137   -2171   98069 1789765 

Coefficients:
                               Value       Std. Error  t value    
(Intercept)                    -41032.0523   5219.4403     -7.8614
floor_area                       2786.9866     31.7158     87.8738
rooms_num                       21215.1095   1081.1512     19.6227
categoryMieszkanie na sprzedaż 138958.6328   3236.8841     42.9298
is_business                     25870.1684   2868.9866      9.0172

Residual standard error: 129200 on 30665 degrees of freedom
  (31 observations deleted due to missingness)

sum(m3$w) / NROW(m3$w)

[1] 0.8637105

plot(m3$y, m3$w, xlab = "Price", ylab = "Huber weight", 
     main = "Distribution of prices and Huber weights")

plot(m3$x[,"floor_area"], m3$w, xlab = "Floor area", ylab = "Huber weight", 
     main = "Distribution of floor area and Huber weights")